Intermediate Differential equations  (Fall 2021)

(Math 405, MWF 10:00-10:50AM)




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Announcements: Midterm test in Week 10 (tentatively).


Review of integration and Key to the practicing problems


Examples for separable equations, exact equations and drawing phase lines


An example for eigenvalues and eigenvectors

Instructor:  Dr. Dashun Xu

Office: 273 Neckers Hall A Wing
Office Hours: MWF 11am-12:20pm, TTh 1:50-2:50pm or by appointment
-mail: Phone: 453-6598

Text Books:

1.      Elementary Differential Equations and Boundary Value Problems, 10th Ed., by Boyce and DiPrima.

2.      Differential Equations with Matlab, 2nd Ed., by B. R. Hunt, R. L. Lipsman, J. E. Osborn, J. M. Rosenberg


Chapter 7, 9 of Textbook 1. If possible, some applications in Mathematical Biology will be included.

Some MATLAB Resources


One midterm and one comprehensive final exams.

Grading Policy:

Your course grade will be computed as follows: 

50% from homework, MATLAB projects and quizzes, 50% from the mid-term exam and the final (25% each).

Letter grades will then be assigned according to the scale:


A, 100-90; B, 89-80; C, 79-70; D, 69-60; F, below 59.

Homework and Projects:

All assignments will be collected every Friday in class and only a few questions in each assignment will be graded. Late homework and projects will not be accepted.



Due Day

 Week 1

Review basic concepts and methods from Math 305


Review of integration and Key to the practicing problems


Examples for separable equations, exact equations and drawing phase lines



Matlab homework


 Week 2

M: 7.1: 3, 6, 8 (please take a look at 7), 16, together with either the set of 17, 18 or the set of 19, 20.


M: 7.1, WF: 7.2

Homework for 7.1 and Matlab homework due this Fri.


Seems that Matlab changed a little bit. So, please change the problem 7 for Mathlab homework into

Y= t^2/ (1+y)

Week 3


W 7.2; F 7.3;

No homework due this week

Week 4


7.2: 4, 8, 11, 16, 22, 25,

7.3: 1, 2, 3, 5; Check the dependence of the vectors given in 7, 8, 9;;


MWF 7.3

Due on Fri.

Week 5


7:3: 15, 18, 21, 24

7.4: 5, 2(a,b,c), 3, optional: 4, 8.


Due on Fri.

Week 6


7.5: Find the general solution for 1, 3, 5


Matlab: draw direction fields for 1,3,5 using computer, and sketch a few trajectories by computer or hand in your direction fields.



MWF 7.4-7.5

Due on Next Mon for Week 6 homework.

Week 7





7.5: 7, 11, 15, 17,


Draw direction field for 7 using Matlab and then on top of it, draw a phase portrait for the system.




MWF 7.5

Due on Fri.

Week 8


7.5: 24, 25, 27; optional: 19, 21, 28


Find the general solutions, sketch phase portrait and Matlab: direction field for 7.6: 2, 3, 11

Find the general solution for

7.6: 7, 9,



MWF 7.6

Due on Fri!!!

Week 9


7.6: 13,15, 17


7.7: 1, 3, 5, 9, 11


homework due on Fri

Week 10



7.8: find the general solution and use Matlab draw the direction field for 1, 3

7.8: Sketch the phase portraits of 1,3 (Please check the direction fields you got )

7.8: find the general solution for 5

7.8: 7(a), 11(a)



A sample exam

Due on Fri.




Week 11

7.9: 1,7 (using method of undetermined coefficients, or diagonalization method); 3,5 (variation of parameters); 9 (any method)





After finishing Chap 7, have the exam.




Currently we are in Week 12


9.1: 1, 2, 4, 5, 6, 10, 11(only a,b,c for 1-11), 13, 15





The homework for 9.1 will not be collected. But I suggest you all try them because they are kind of review problems for the exam.



Exam on next Mon due to no class on Fri

Week 13


9.2: 5(a), 6 (a); 15(a),22(a);

Matlab: 9.2: 5 (bc), 6(bc), 15(b), 22(b)

Optional problems for 9.2, 19(a), 24, 25.

Week 14


9.3: 1, 2, 5(a,b,c), 7(a,b,c), 11(a,b,c)

Matlab: draw the direction fields and then on top of them sketch phase portraits for 5,7,11(d)



Week 15

Review 9.1 and 9.2, 9.3, midterm sample and actual exams, plus

Sample exam and related problems

Final exam: 10:1512:15pm, Dec 10, Fri. EGRA 420

Make-up Policy:

Make-up exams will only be granted to students who have convincing excuses and have informed me in advance. And proper documentation is needed.


Regular attendance to the lectures is strongly advised. You will be responsible for all the material presented in the class, regardless of whether or not you were present.

Study Hint:


Find at least one or two other students from the class with whom you can regularly do homework and prepare for exams. Your classmates are perhaps the least used and arguably your best resource. An efficient and effective study group will streamline homework and study time, reduce the need for attendance at office hours, and greatly improve your written and spoken communication. The best time to use your classmates as study/homework partners is after you have made an honest effort on your own to solve the problems using your own wits, knowledge, and experience. When you encounter an unsolvable problem, don't give up too soon on it. Being stumped is an opportunity for mathematical growth and insight, even if you never solve the problem on your own. If you seek help prematurely, you will never know if you could have solved a tough problem without outside assistance.


Syllabus Attachment:



                                    Last modified Aug.13, 2021 by Dashun Xu..